A disc is rolling without slipping with angular velocity `omega`. P and Q are two points equidistant from the centre C. the order of magnitude fo velocity is

Options

A. `V_(q) gt V_(C) gt V_(F)`
B. `V_(p) gt V_(C) > V_(Q)`
C. `V_(P)= V_(C), V_(Q) = V_(C)//2`
D. `V_(P) lt V_(C) gt V_(q)`

Answer

A

Explanation

The rolling disc can be considered as pure rotation about point of contact O. In this case point O will act as instantaneous centre of rotation of disc.
Hence velocity of point `P,V_(p) = omegar_(1)`

Velocity of point, Q, `v_(Q) = omega r_(2)`
velocity of point C, `v_(C) = omegaR`
`r_(2) gt R gt r_(1) rArr v_(Q) gt v_(C) gt v_(P)` .